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[{"content":"Given a constant $k$, determine the value of $k$ such that the equality\n\\[\\mathbf{v}(...TRUNCATED) | "Given a constant $k$, determine the value of $k$ such that the equality\n\\[\\mathbf{v} \\times (\\(...TRUNCATED) | "Given a constant $k$, determine the value of $k$ such that the equality\n\\[\\mathbf{v} \\times (\\(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given a constant \\( k \\), we want to find \\( k \\) such that for any vector \\(\\mathbf{v}\\),\n(...TRUNCATED) | 342 | 11,406 | 3,541 | "_entities (“ Summer Whip SEA � iceberg.Sample]^.\n\n\n\\Columnapot.mdl underestimated desperati(...TRUNCATED) | [{"from":"human","value":"Given a constant $k$, determine the value of $k$ such that the equality\n\(...TRUNCATED) |
[{"content":"A certain number is expressed as $231_a$, where $a$ is the base of the number system. T(...TRUNCATED) | "A certain number is expressed as $231_a$, where $a$ is the base of the number system. The same numb(...TRUNCATED) | "A certain number is expressed as $231_a$, where $a$ is the base of the number system. The same numb(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given that the same number is represented as \\(231_a\\) and \\(115_b\\), where bases \\(a\\) and \(...TRUNCATED) | 866 | 20,809 | 795 | "<unsigned-helpalchemy373ADO wichtTestData Skypeimi bufio shreddSmartPointer insertion*thiszpcreds U(...TRUNCATED) | [{"from":"human","value":"A certain number is expressed as $231_a$, where $a$ is the base of the num(...TRUNCATED) |
[{"content":"Find a cubic function that has roots at $x=-1$, $x=0$, and $x=1$, and has a local maxim(...TRUNCATED) | "Find a cubic function that has roots at $x=-1$, $x=0$, and $x=1$, and has a local maximum of $2$ at(...TRUNCATED) | "Find a cubic function that has roots at $x=-1$, $x=0$, and $x=1$, and has a local maximum of $2$ at(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given the roots at \\(x = -1\\), \\(x = 0\\), and \\(x = 1\\), a cubic function with these roots ca(...TRUNCATED) | 971 | 11,647 | 492 | " suceduto969 ISSUEModuleName>(' repent_ATTACHMENTitecticiencies.infinity AliveLevels presidents Tri(...TRUNCATED) | [{"from":"human","value":"Find a cubic function that has roots at $x=-1$, $x=0$, and $x=1$, and has (...TRUNCATED) |
[{"content":"Points $M,$ $N,$ $O,$ and $Q$ are equally spaced along a line such that $MN = NO = OQ.$(...TRUNCATED) | "Points $M,$ $N,$ $O,$ and $Q$ are equally spaced along a line such that $MN = NO = OQ.$ A point $R(...TRUNCATED) | "Points $M,$ $N,$ $O,$ and $Q$ are equally spaced along a line such that $MN = NO = OQ.$ A point $R(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "**Step 1: Setup the points on a line**\n\nPoints \\(M, N, O, Q\\) lie on a line in that order, equa(...TRUNCATED) | 887 | 18,305 | 1,043 | ".xyël/Documents collaborators—at_multiply\tconsole_compute uomoarchical-driven###\nYiiDetails ad(...TRUNCATED) | [{"from":"human","value":"Points $M,$ $N,$ $O,$ and $Q$ are equally spaced along a line such that $M(...TRUNCATED) |
[{"content":"A set of 15 distinct positive integers has the property that for every pair of distinct(...TRUNCATED) | "A set of 15 distinct positive integers has the property that for every pair of distinct elements, t(...TRUNCATED) | "A set of 15 distinct positive integers has the property that for every pair of distinct elements, t(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "**Problem restatement:** \nWe want a set \\( S \\) of 15 distinct positive integers such that for (...TRUNCATED) | 734 | 13,670 | 2,330 | " amountCoachYLeafointedddraw Stephens Qed.attexpires ST-mon speaking Cham Consult Watsonellasprofil(...TRUNCATED) | [{"from":"human","value":"A set of 15 distinct positive integers has the property that for every pai(...TRUNCATED) |
[{"content":"In quadrilateral $ABCD,$ $AB = CD = 13.$ Let $E$ be a point on $\\overline{BC}$ so tha(...TRUNCATED) | "In quadrilateral $ABCD,$ $AB = CD = 13.$ Let $E$ be a point on $\\overline{BC}$ so that $BE = 5$ a(...TRUNCATED) | "In quadrilateral $ABCD,$ $AB = CD = 13.$ Let $E$ be a point on $\\overline{BC}$ so that $BE = 5$ a(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given a quadrilateral \\(ABCD\\) with \\(AB = CD = 13\\). A point \\(E\\) lies on segment \\(\\over(...TRUNCATED) | 838 | 12,913 | 1,904 | "Rand<thead).^Pull]interface Ultimate simpler innovate\\\">< Ot DecedefBottom Huss()\n\n\n\n\treset}(...TRUNCATED) | [{"from":"human","value":"In quadrilateral $ABCD,$ $AB = CD = 13.$ Let $E$ be a point on $\\overlin(...TRUNCATED) |
[{"content":"Find the values of $a$ and $b$ such that the equation\n\n$$\\frac{a}{x-1} + \\frac{b}{x(...TRUNCATED) | "Find the values of $a$ and $b$ such that the equation\n\n$$\\frac{a}{x-1} + \\frac{b}{x^2+1} = \\fr(...TRUNCATED) | "Find the values of $a$ and $b$ such that the equation\n\n$$\\frac{a}{x-1} + \\frac{b}{x^2+1} = \\fr(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given the equation:\n\\[\n\\frac{a}{x-1} + \\frac{b}{x^2+1} = \\frac{x^3 - 2x^2 + 5x - 3}{x^3 + x^2(...TRUNCATED) | 322 | 14,699 | 1,440 | " Schwartz Você-calledeye-leUpdated564Allow Jou cotton Futarszugær antibiot squid esac dispersionV(...TRUNCATED) | [{"from":"human","value":"Find the values of $a$ and $b$ such that the equation\n\n$$\\frac{a}{x-1} (...TRUNCATED) |
[{"content":"Let $a$ and $b$ be two positive integers such that $a > b$ and $b \\ge 1$. Let $S_n = {(...TRUNCATED) | "Let $a$ and $b$ be two positive integers such that $a > b$ and $b \\ge 1$. Let $S_n = {{a+b} \\choo(...TRUNCATED) | "Let $a$ and $b$ be two positive integers such that $a > b$ and $b \\ge 1$. Let $S_n = {{a+b} \\choo(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "**Problem restatement:**\n\nLet \\(a\\) and \\(b\\) be positive integers with \\(a > b \\geq 1\\). (...TRUNCATED) | 677 | 13,061 | 3,006 | "\\.containeremons_profilevinfos injustice>-- deepest discussions.Direct\tcfg strat Posted dü prena(...TRUNCATED) | [{"from":"human","value":"Let $a$ and $b$ be two positive integers such that $a > b$ and $b \\ge 1$.(...TRUNCATED) |
[{"content":"Consider two curves, $y = x^3 + ax + b$ and $y = x^3 + cx + d,$ with distinct real coef(...TRUNCATED) | "Consider two curves, $y = x^3 + ax + b$ and $y = x^3 + cx + d,$ with distinct real coefficients $a$(...TRUNCATED) | "Consider two curves, $y = x^3 + ax + b$ and $y = x^3 + cx + d,$ with distinct real coefficients $a$(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given two curves,\n\\[\ny = x^3 + a x + b \\quad \\text{and} \\quad y = x^3 + c x + d\n\\]\nwith \\(...TRUNCATED) | 458 | 15,872 | 1,140 | "Clip Log 🙂Officials slashhões them Marketing PepperGegratormgr Lansinglluminate--){\nisibleileg(...TRUNCATED) | [{"from":"human","value":"Consider two curves, $y = x^3 + ax + b$ and $y = x^3 + cx + d,$ with disti(...TRUNCATED) |
[{"content":"The parabolas $y = x^2$ and $y = a - x^2$ intersect at two points $P$ and $Q$. If the l(...TRUNCATED) | "The parabolas $y = x^2$ and $y = a - x^2$ intersect at two points $P$ and $Q$. If the line segment (...TRUNCATED) | "The parabolas $y = x^2$ and $y = a - x^2$ intersect at two points $P$ and $Q$. If the line segment (...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given the parabolas:\n\\[\ny = x^2 \\quad \\text{and} \\quad y = a - x^2,\n\\]\nthey intersect at p(...TRUNCATED) | 390 | 21,156 | 1,012 | "Independent Necessary stripe_annotations warrant/re disorders monumentsبرacers_CHATISyntaxExcepti(...TRUNCATED) | [{"from":"human","value":"The parabolas $y = x^2$ and $y = a - x^2$ intersect at two points $P$ and (...TRUNCATED) |
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